Editing Identity function (section)

==Properties==
*The identity function is a [[linear map|linear operator]] when applied to [[vector space]]s.<ref>{{Citation|last=Anton|first=Howard|year=2005|title=Elementary Linear Algebra (Applications Version)|publisher=Wiley International|edition=9th}}</ref>
*In an {{mvar|n}}-[[dimension (vector space)|dimensional]] [[vector space]] the identity function is represented by the [[identity matrix]] {{math|''I''<sub>''n''</sub>}}, regardless of the [[basis (linear algebra)|basis]] chosen for the space.<ref>{{cite book|title=Applied Linear Algebra and Matrix Analysis|author=T. S. Shores|year=2007|publisher=Springer|isbn=978-038-733-195-9|series=Undergraduate Texts in Mathematics|url=https://books.google.com/books?id=8qwTb9P-iW8C&q=Matrix+Analysis}}</ref>
*The identity function on the positive [[integer]]s is a [[completely multiplicative function]] (essentially multiplication by 1), considered in [[number theory]].<ref>{{cite book|title=Number Theory through Inquiry|author1=D. Marshall |author2=E. Odell |author3=M. Starbird |year=2007|publisher=Mathematical Assn of Amer|isbn=978-0883857519|series=Mathematical Association of America Textbooks}}</ref> 
*In a [[metric space]] the identity function is trivially an [[isometry]]. An object without any [[symmetry]] has as its [[symmetry group]] the [[trivial group]] containing only this isometry (symmetry type {{math|C<sub>1</sub>}}).<ref>{{aut|James W. Anderson}}, ''Hyperbolic Geometry'', Springer 2005, {{isbn|1-85233-934-9}}</ref>
*In a [[topological space]], the identity function is always [[Continuous_function#Continuous_functions_between_topological_spaces|continuous]].<ref>{{Cite book|last=Conover|first=Robert A.|url=https://books.google.com/books?id=KCziAgAAQBAJ&q=identity+function+is+always+continuous&pg=PA65|title=A First Course in Topology: An Introduction to Mathematical Thinking|date=2014-05-21|publisher=Courier Corporation|isbn=978-0-486-78001-6|pages=65|language=en}}</ref>
*The identity function is [[Idempotence|idempotent]].<ref>{{Cite book|last=Conferences|first=University of Michigan Engineering Summer|url=https://books.google.com/books?id=AvAfAAAAMAAJ&q=The+identity+function+is+idempotent.|title=Foundations of Information Systems Engineering|date=1968|language=en|quote=we see that an identity element of a semigroup is idempotent.}}</ref>